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Sebuah matriks dikatakan orthogonal jika A − 1 = A T . J ika A = ⎝ ⎛ ​ 7 3 ​ b 7 2 ​ ​ 7 2 ​ 7 3 ​ 7 6 ​ ​ a 7 2 ​ c ​ ⎠ ⎞ ​ adalah matriks orthogonal makaa 2 + b 2 + c 2 = ....

Sebuah matriks dikatakan orthogonal jika adalah matriks orthogonal maka a2 + b2 + c2 = ....

  1. 81 over 49

  2. 72 over 49

  3. 45 over 49

  4. 36 over 49

  5. 9 over 49

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I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Pembahasan

U n t u k space s e m b a r a n g space m a t r i k s space p e r s e g i space y a n g space m e m i l i k i space i n v e r s space s e l a l u space b e r l a k u space A A to the power of negative 1 end exponent equals I space T e t a p i space k a r e n a space p a d a space s o a l space i n i space A to the power of negative 1 end exponent space equals space A to the power of T comma space m a k a A A to the power of T space end exponent equals I open parentheses table row cell 3 over 7 end cell cell 2 over 7 end cell a row b cell 3 over 7 end cell cell 2 over 7 end cell row cell 2 over 7 end cell cell 6 over 7 end cell c end table close parentheses open parentheses table row cell 3 over 7 end cell b cell 2 over 7 end cell row cell 2 over 7 end cell cell 3 over 7 end cell cell 6 over 7 end cell row a cell 2 over 7 end cell c end table close parentheses equals open parentheses table row 1 0 0 row 0 1 0 row 0 0 1 end table close parentheses D e n g a n space m e l a k u k a n space p e r k a l i a n space y a n g space s e s u a i space d i d a p a t space 9 over 49 plus 4 over 49 plus a squared equals 1 left right double arrow a squared equals 36 over 49 b squared plus 9 over 49 plus 4 over 49 equals 1 left right double arrow b squared equals 36 over 49 4 over 49 plus 36 over 49 plus c squared equals 1 left right double arrow c squared equals 9 over 49 S e h i n g g a space a squared plus b squared plus c squared equals 81 over 49

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